1. **State the problem:** Dr. Kingsley mixed 60 ounces of a 20% gold alloy with some amount of a 30% gold alloy to get a 24% gold alloy. We need to find how many ounces of the 30% alloy were used. 2. **Set variables:** Let $x$ be the ounces of the 30% gold alloy used. 3. **Write the gold content equation:** The total gold from both alloys equals the gold in the final mixture. $$0.20 \times 60 + 0.30 \times x = 0.24 \times (60 + x)$$ 4. **Calculate the left side:** $$12 + 0.30x = 0.24(60 + x)$$ 5. **Distribute the right side:** $$12 + 0.30x = 14.4 + 0.24x$$ 6. **Bring like terms together:** $$12 + 0.30x - 0.24x = 14.4$$ $$12 + 0.06x = 14.4$$ 7. **Isolate $x$:** $$0.06x = 14.4 - 12$$ $$0.06x = 2.4$$ 8. **Solve for $x$:** $$x = \frac{2.4}{0.06}$$ 9. **Simplify the fraction:** $$x = \frac{\cancel{2.4}}{\cancel{0.06}} = 40$$ 10. **Answer:** Dr. Kingsley used **40 ounces** of the 30% gold alloy.